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I have to deal with a statistical issue in a study, specially with the use of Kaplan-Meier estimator in the case of non independent observations.

Background of the study: We follow-up patients (N = 500) who underwent ear surgery (cochlear implant). There are two type of implants (A and B) and the objective is to describe luxation of the implant in both groups.

The issue here is that some patients underwent surgery on both ears and others on only one ear (so we have 800 observations). I can't use KM estimator (and log-rank test) because all my observations are not independent. How should I deal with this issue ?

I have done some research but I have not found a clear answer about alternative of KM estimator in a context of dependent observations.

I perform my analyses with R.

Thank you for your advices !

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  • $\begingroup$ Can you detail why your observations are not independent? Does luxation of the implant of a patient affect the probability of luxation of the implant in another patient? Or are your obervations at the ear-level, so there are patients with two observations in your data (the ones that underwent surgery in both ears), and the luxation in one ear affect the probability of luxation in another ear? $\endgroup$ Commented Oct 17, 2023 at 12:10

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This page discusses how to handle this situation for a Kaplan-Meier curve. The correlations within individuals affect the variance of the Kaplan-Meier estimate, not the estimate itself. Annotate the cases with an id variable representing the individual. Software then can take that into account to produce robust variance estimates. See the help page for the R survival package survfit.formula() function.

For comparing the two types of implants, proceed similarly with a Cox proportional hazards model. Use implant type as a predictor (along with other desired covariates) and your id variable to distinguish individuals. With the R coxph() function, specify that you want a cluster variance estimate.

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    $\begingroup$ Thank you for your clear advice. I have found a R library prodlim. This library has a function called prodlim which replaces Greenwood's variance formula for Ying and Wei (1994)'s formula where you are in a situation with correlated data. $\endgroup$
    – Adrian
    Commented Jul 30, 2022 at 10:46

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